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PM003 - Aula 4
Curvas de Nível
f(x,y)=k
f[x_, y_] := x^2 + y^2
grafico = ParametricPlot3D[{x, y, f[x, y]},
{x, -2, 2}, {y, -2, 2}, Mesh → None, PlotStyle → Opacity[0.7]]
Printed by Wolfram Mathematica Student Edition
Show[grafico, ParametricPlot3D[{x, y, 1}, {x, -2, 2},
{y, -2, 2}, Mesh → None, PlotStyle → {Green, Opacity[0.7]}],
ParametricPlot3D[{Cos[t], Sin[t], 1}, {t, 0, 2 π}, PlotStyle → {Black, Thick}],
ParametricPlot3D[{Cos[t], Sin[t], 0}, {t, 0, 2 π}, PlotStyle → {Black, Thick}]]
ContourPlot[f[x, y] ⩵ 1, {x, -2, 2}, {y, -2, 2}](*Plota uma curva de nível*)
-2 -1 0 1 2
-2
-1
0
1
2
2 Aula 08_09.nb
Printed by Wolfram Mathematica Student Edition
AnimateShowgrafico, ParametricPlot3D[{x, y, k}, {x, -2, 2}, {y, -2, 2},
Mesh → None, PlotStyle → {Green, Opacity[0.7]}], ParametricPlot3D
 k Cos[t], k Sin[t], k, {t, 0, 2 π}, PlotStyle → {Black, Thick}, {k, 0, 4}
k
Showgrafico, , 
f[x_, y_] := Sin[x y]
grafico = ParametricPlot3D[{x, y, f[x, y]},
{x, -3, 3}, {y, -3, 3}, Mesh → None, PlotStyle → Opacity[0.7]]
Show[grafico, ParametricPlot3D[{x, y, 0}, {x, -3, 3},
{y, -3, 3}, Mesh → None, PlotStyle → {Green, Opacity[0.7]}]]
Aula 08_09.nb 3
Printed by Wolfram Mathematica Student Edition
ContourPlot[f[x, y], {x, -3, 3}, {y, -3, 3}]
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
g[x_, y_, z_] := x^2 + y^2 + z^2
ContourPlot3D[g[x, y, z] ⩵ 9, {x, -5, 5}, {y, -5, 5}, {z, -5, 5}]
4 Aula 08_09.nb
Printed by Wolfram Mathematica Student Edition
Limite
p[x_, y_] := x^2 y + 2 y
Limit[Limit[p[x, y], x → 1], y → 2]
6
Aula 08_09.nb 5
Printed by Wolfram Mathematica Student Edition